Tuesday, August 25, 2015

A reply paper published today in PNAS "identifies a causal relationship between cosmic rays (CRs) and interannual variation in global temperature (ΔGT)." The authors find a "robust" cosmic ray-global temperature relationship, as demonstrated in Fig. 1 below, and thus provide further corroboration of the solar/cosmic ray theory of climate of Svensmark et al.

Tsonis et al. (1) recently used convergent cross mapping (CCM) (2) to identify a causal relationship between cosmic rays (CRs) and interannual variation in global temperature (ΔGT). Subsequently, Luo et al. (3) questioned this finding using the Clark implementation of CCM (version 1.0 of the multispatial CCM package).* This version of the CCM code, which has since been debugged by Clark, unfortunately contains errors that are not in the original rEDM software package that Tsonis et al. used.† Thus, though well-intentioned, the Luo et al. (3) analysis is incorrect.

However, despite the erroneous analysis, Luo et al. (3) raise valid concerns over the robustness of the finding. Here, we demonstrate that the CR effect on ΔGT is robust to reasonable measures of global temperature, and clarify technical details for determining significance with CCM.

CCM uses cross-map prediction as a metric for causality: a variable y has a causal effect on x when the attractor manifold constructed from lags of x can estimate values of y. Causality is established when cross-map performance increases with library size, L, and is significantly better than an appropriate null model at the largest L. Sugihara et al. (2) were the first (to our knowledge) to construct an effective test for causality using these ideas.

As Luo et al. suggest, different ways of subsampling the data to construct libraries, can yield slightly different values for ρ. Indeed, the rEDM software package provides three different sampling methods: (i) taking contiguous segments of length L from among the available x as in ref. 2, (ii) taking bootstrap samples with replacement as in ref. 4, and (iii) taking random subsamples without replacement as in ref. 1.

There are reasons for choosing one method over another. For example, method i should not be used to examine a strongly autocorrelated time series and either ii or iii would be preferable as they sample libraries without consideration for time. Also note that the rEDM cross-validation procedure addresses Luo et al.’s (3) concern over having the pair (xj, yj) in the library when predicting yj.

The second issue raised by Luo et al. (3) is the robustness of the CR–ΔGT relationship to different temperature data records. As discussed in the Intergovernmental Panel on Climate Change AR5 report, HadCRUT4 is the most primary and credible global temperature record (5), with reasonable uncertainty estimates. Other records such as Goddard Institute for Space Studies (GISS) and National Climatic Data Center (NCDC) data have periods that fall outside the 90% confidence interval of HadCRUT4 (see figure 2.19 of ref. 5) and are not as highly regarded. This is partly due to infilling, spatial averaging, or interpolation: smoothing practices known to obscure nonlinearity (6), which would diminish residual interannual CR effects, especially if first differenced time series are used. Thus, among available records, the HadCRUT4 and HadCRUT3v time series are sensible choices for this study, whereas GISS and NCDC are not.

Fig. 1 examines the CR–ΔGT relationship using all three library-sampling methods as well as the four temperature time series examined by Luo et al. (3). As shown, this relationship is robust to both library sampling and reasonable data choices. We note that the significance of causality is determined only at the largest library size, with convergence being a further necessary condition to demonstrate causation.

CCM results for four different global temperature time series (HadCRUT3v as in ref. 1, HadCRUT4, GISS, NCDC) and using three different library-sampling methods (contiguous segments, bootstraps, and subsamples). For each panel, the blue line denotes the effect of CRs on interannual temperature variability (“ΔGT xmap CR”), whereas the red line denotes causality in the opposite direction (“CR xmap ΔGT”). The red and blue regions denote the lower 95% quantile for null distributions generated using phase-randomized surrogates. Other parameters were the same as in ref. 1 (selection of E, τ, and prediction delay), but due to an indexing error in ref. 1, data from 1899–2011 were used, and the prediction delay is −1 (instead of −2) for HadCRUT3v xmap CR. Medians over different library samples were computed as a robust measure of central tendency to account for nonnormal and system-specific distributions of ρ. Both HadCRUT3v and HadCRUT4 show the influence of CRs, whereas the more processed GISS and NCDC time series fail to do so. Conversely, there is no evidence for an effect of temperature on CRs (as expected).

Saturday, August 22, 2015

An important new paper published in Advances in Space Research determines that the Earth surface temperature (as well as the surface temperatures of 5 other rocky planets in our solar system) can be very accurately determined (R2 = 0.9999! & tiny standard errorσ=0.0078) solely on the basis of two variables: 1) atmospheric pressure at the surface, and 2) solar irradiance at the top of the atmosphere, and without any consideration of any greenhouse gas concentrations or 'radiative forcing' from greenhouse gases whatsoever. Thus, the paper adds to the works of at least 40 others (partial list below) who have falsified the Arrhenius radiative theory of catastrophic global warming from increased levels of CO2, and also thereby demonstrated that the Maxwell/Clausius/Carnot/Boltzmann/Feynman atmospheric mass/gravity/pressure greenhouse theory is instead the correct explanation of the 33C greenhouse effect on Earth, and which is independent of "radiative forcing" from greenhouse gases. Using observed data from the planets Earth, Venus, the Moon, Mars, Titan, and Triton, the authors,

"apply the Dimensional Analysis (DA) methodology to a well-constrained data set of six celestial bodies representing highly diverse physical environments in the solar system, i.e. Venus, Earth, the Moon, Mars, Titan (a moon of Saturn), and Triton (a moon of Neptune). Twelve prospective relationships (models) suggested by DA are investigated via non-linear regression analyses involving dimensionless products comprised of solar irradiance, greenhouse-gas partial pressure/density and total atmospheric pressure/density as forcing variables, and two temperature ratios as dependent (state) variables. One non-linear regression model is found to statistically outperform the rest by a wide margin. Our analysis revealed that GMATs [Global Mean Atmospheric Temperatures] of rocky planets can accurately be predicted over a broad range of atmospheric conditions [0% to over 96% greenhouse gases] and radiative regimes only using two forcing variables: top-of-the-atmosphere solar irradiance and total surface atmospheric pressure [a function of atmospheric mass & gravity]. The new model displays characteristics of an emergent macro-level thermodynamic relationship heretofore unbeknown to science that deserves further investigation and possibly a theoretical interpretation."

Fig. 4.

Dependence of the relative atmospheric thermal enhancement (Ts/Tna) on mean surface air pressure according to Eq. (10a) derived from data representing a broad range of planetary environments in the Solar System. Saturn’s moon Titan has been excluded from the regression analysis leading to Eq. (10a). Error bars of some bodies are not clearly visible due to their small size relative to the scale of the axes. See Table 2 for the actual error estimates.

"The above comparisons indicate that Eq. (10b) rather accurately reproduces the observed variation of mean surface temperatures across a wide range of planetary environments characterized in terms of solar irradiance (from 1.5 W m-2 to 2,602 W m-2), total atmospheric pressure (from near vacuum to 9,300 kPa), and greenhouse-gas concentrations (from 0.0% to over 96% per volume). While true that Eq. (10a) is only based on data from 6 planetary bodies, one should keep in mind that these represent all objects in the Solar System meeting our criteria (discussed in Section 2.3) for the quality of available data. The fact that only one of the investigated twelve non-linear regressions yielded a tight relationship suggests that Model 12 might be describing a macro-level thermodynamic property of planetary atmospheres heretofore unbeknown to science . A function of such predictive skill spanning the breadth of the Solar System may not be just a result of chance. Indeed, complex natural systems consisting of myriad interacting agents have been known to exhibit emergent behaviors at higher levels of hierarchical organization that are amenable to accurate modeling using top-down statistical approaches (e.g. Stolk et al. 2003). Equation (10) also displays several other characteristics that lend further support to the above conjecture."

Comparison of the two best-performing regression models according to statistical scores presented inTable 5. Vertical axes use linear scale to better illustrate the difference in skills between the models. Added: The top model incorporates greenhouse gas partial pressures and has a standard error over 20 times worse than the bottom model which does not consider greenhouse gas concentrations or radiative forcing whatsoever.

Fig. 5.

Absolute differences between predicted average global surface temperatures (Eq. 10b) and observed GMATs (Table 2) for studied celestial bodies. Titan represents an independent data point, since it was excluded from the non-linear regression analysis leading to Eq. (10a).

Added: The surface temperatures of 5 planets are determined within hundredths of degrees C using the Eqn 10a as a sole function of surface pressure and solar insolation.

Fig. 7.

a) Dry adiabatic response of the air/surface temperature ratio to pressure changes in the free atmosphere according to Poisson’s formula (Eq. 12). The reference pressure is arbitrarily assumed to be po=100 kPa;b) The SB radiation law expressed as a response of a blackbody temperature ratio to variation in photon pressure (see text for details). Note the similarity in shape between these two curves and the one portrayed in Fig. 4 depicting Eq. (10a).

The authors have used a new empirical non-linear regression method of determining the gravito-thermal greenhouse effect on 6 planets, and "might be describing a macro-level thermodynamic property of planetary atmospheres heretofore unbeknown to science," but are apparently unaware of and do not cite any of the over 36 scientific works/papers (partial list below) which have described the theoretical basis of the same 33C Maxwell/Clausius/Carnot gravito-thermal effect of atmospheric pressure, some of which also utilize the Poisson relation as illustrated in Fig 7. from the paper above.

Only one possible explanation of the 33C 'greenhouse' effect temperature gradient on Earth can be possible, otherwise the greenhouse effect would be twice as large (i.e. 66C):

2) The 33C Maxwell/Clausius/Carnot gravito-thermal effect, proven by this new paper and the works/papers of at least 36 others (and very accurately predicts the surface and atmospheric temperatures of all rocky planets with an atmosphere in our solar system):

Highlights

Dimensional Analysis is used to model the average temperature of planetary bodies.

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The new model is derived via regression analysis of measured data from 6 bodies.

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Planetary bodies used by the model are Venus, Earth, Moon, Mars, Titan and Triton.

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Two forcing variables are found to accurately predict mean planetary temperatures.

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The predictor variables include solar irradiance and surface atmospheric pressure.

Abstract

The Global Mean Annual near-surface Temperature (GMAT) of a planetary body is an expression of the available kinetic energy in the climate system and a critical parameter determining planet’s habitability. Previous studies have relied on theory-based mechanistic models to estimate GMATs of distant bodies such as extrasolar planets. This ‘bottom-up’ approach oftentimes relies on case-specific parameterizations of key physical processes (such as vertical convection and cloud formation) requiring detailed measurements in order to successfully simulate surface thermal conditions across diverse atmospheric and radiative environments. Here, we present a different ‘top-down’ statistical approach towards the development of a universal GMAT model that does not require planet-specific empirical adjustments. Our method is based on Dimensional Analysis (DA) of observed data from the Solar System. DA provides an objective technique for constructing relevant state and forcing variables while ensuring dimensional homogeneity of the final model. Although widely utilized in some areas of physical science to derive models from empirical data, DA is a rarely employed analytic tool in astronomy and planetary science. We apply the DA methodology to a well-constrained data set of six celestial bodies representing highly diverse physical environments in the solar system, i.e. Venus, Earth, the Moon, Mars, Titan (a moon of Saturn), and Triton (a moon of Neptune). Twelve prospective relationships (models) suggested by DA are investigated via non-linear regression analyses involving dimensionless products comprised of solar irradiance, greenhouse-gas partial pressure/density and total atmospheric pressure/density as forcing variables, and two temperature ratios as dependent (state) variables. One non-linear regression model is found to statistically outperform the rest by a wide margin. Our analysis revealed that GMATs of rocky planets can accurately be predicted over a broad range of atmospheric conditions and radiative regimes only using two forcing variables: top-of-the-atmosphere solar irradiance and total surface atmospheric pressure. The new model displays characteristics of an emergent macro-level thermodynamic relationship heretofore unbeknown to science that deserves further investigation and possibly a theoretical interpretation.